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Finiteness Properties of Minimax and \( \mathfrak{a} \)-Minimax Generalized Local Cohomology Modules

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Ukrainian Mathematical Journal Aims and scope

Let R be a commutative Noetherian ring with nonzero identity, let a be an ideal of R, and let M and N be two (finitely generated) R-modules. We prove that \( H_{\mathfrak{a}}^i\left( {M,N} \right) \) is a minimax \( \mathfrak{a} \)-cofinite R-module for all i < t, t\( {{\mathbb{N}}_0} \), if and only if \( H_{\mathfrak{a}}^i{{\left( {M,N} \right)}_p} \) is a minimax \( {R_{\mathfrak{p}}} \) -module for all i < t. We also show that, under certain conditions, \( \mathrm{Ho}{{\mathrm{m}}_R}\left( {\frac{R}{\mathfrak{a}},H_{\mathfrak{a}}^t\left( {M,N} \right)} \right) \) is minimax (t\( {{\mathbb{N}}_0} \)). Finally, we study necessary conditions for \( H_{\mathfrak{a}}^i\left( {M,N} \right) \) to be \( \mathfrak{a} \)-minimax.

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Published in Ukrains’kyi Matematychnyi Zhurnal, Vol. 65, No. 6, pp. 796–801, June, 2013.

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Kianezhad, A., Taherizadeh, A.J. Finiteness Properties of Minimax and \( \mathfrak{a} \)-Minimax Generalized Local Cohomology Modules. Ukr Math J 65, 884–890 (2013). https://doi.org/10.1007/s11253-013-0825-3

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  • DOI: https://doi.org/10.1007/s11253-013-0825-3

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